What has perplexed me for some time is the inability of the Ukrainian forces to dislodge the Russians from the west bank of the Dnieper River. This area is several thousand square kilometers that is occupied by 6 to 10 BTG so maybe 10,000 combat troops. Hardly an overwhelming force given that there are two major centers that need to be defended as well as the long front line of contact. It would seem to me the current effort of pushing in from the perimeter is just going to get the bridges blown as the Russians retreat over them to the east bank. Another strategy seeming to take place is to destroy/disrupt the supply chain and command structure and force the Russians to withdraw. This has the appeal of less bloodshed and destruction but likely the Russians will pull the bridges down as they pull back and they live to fight another day.
Taking a page from history, much of the current fighting is taking place in the same area as in 1942/3. The Germans were very adept at forming heavily armed mobile battle groups and driving through the front line in narrow breakthroughs to secure bridges deep behind the lines preceding an offensive. Fighting was avoided as much as possible, relying on speed and surprise on the initial penetration. They would set up a hedgehog at the target and hold on till the main forces arrived. Sometimes even driving a heavily armed supply column through to the hedgehog.
If the Ukrainians want the chance of keeping the bridges intact it would seem this is the only option. Do it at Kherson and Nova Kakhovka at the same time. Successful capture of the river crossings would feed panic in the front line forces. Its possible the front lines would collapse as the Russians stream back trying to get across the river. Ukrainians advance in the confusion and collapse the pocket of troops trapped on the west bank. The Dnieper is quite wide upstream of Nova Kakhovka and maybe those river patrol boats would play a role here. It is a risky, high payoff operation...the question is do they have the highly mobile armored forces to pull it off?